The frequency of light emitted by a moving source is shifted by a factor proportional to its velocity. We find that this Doppler shift requires the existence of a paradoxical effect: that a moving atom radiating in otherwise empty space feels a net or average force acing against its direction motion and proportional in magnitude to is speed. Yet there is no preferred rest frame, either in relativity or in Newtonian mechanics, so how can there be a vacuum friction force?